Question

A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of the field is changing, so that an emf of 0.65 V and a current of 3.8 A are induced in the coil. The wire is the re-formed into a single-turn square coil, which is used in the same magnetic field (again perpendicular to the plane of the coil and with a magnitude changing at the same rate). What emf and current are induced in the square coil?

Answer 1

`E_(square)=0.51v`

`i_(square)=2.98A`

Step-by-step explanation:

`E_(mf)=-N*(d\alpha)/(dt)`

`E_(mf)=-N*A*(d\beta)/(dt)`

`N=1`

`E_(circle)=A_(circle)*(d\beta)/(dt)`

`E_(square)=E_(circle)*(A_(square))/(A_(circle))`

`E_(square)=E_(circle)(((\pi^2)/(4)*r^2)/(\pi*r^2))`

`E_(square)=E_(circle)*(\pi)/(4)`

`E_(square)=0.65v*(\pi)/(4)`

`E_(square)=0.51v`

`i_(square)=i_(circle)*(E_(square))/(E_(circle))`

`i_(square)=3.8A*(0.51v)/(0.65v)`

`i_(square)=2.98A`